Prim grows a tree from a start node instead of scanning the full edge list. On this distinct-weight graph, it reaches the same unique MST that Kruskal found.
highlighted = computed this step
Grow from A
Prim adds 5 edges starting from A. Motivation: Prim keeps one connected visited set and grows it by the cheapest exact crossing edge.
Prim additions=5
Same total
The Prim tree total is 19. Why: the recomputed edge set is identical to Kruskal's MST edge set, even though the decision order is different.
w(TPrim)=19
Unique tree
Interpretation: distinct weights make the MST unique in this instance, so two different greedy procedures land on the same certified tree.
distinct weights⇒same MST here
Diagram note
Certificate note: the graph marks the recomputed tree edge role; Prim order and Kruskal order are different procedures with the same final tree here. Pixel positions are rounded for layout; every number shown is exact.